PROGRESSIONS OF STUDENTS’ MENTAL MODELS OF MAGNETISM
ACROSS SCALE
David Sederberg[1,5], Anna-Leena Latvala[2,7], Anssi Lindell[3,6], Lynn Bryan[1,4,8] &
Jouni Viiri[2,9]
Department of Curriculum and Instruction, Purdue University, USA
Department of Teacher Education, University of Jyväskylä, Finland
[3]
Department of Physics, University of Jyväskylä, Finland
[4]
Department of Physics, Purdue University, USA
E-mail: [5]dsederbe@purdue.edu, [6]anssi.lindell@edu.jyu.fi, [7]anna-leena.m.latvala@jyu.fi,
[8]
labryan@purdue.edu, [9]jouni.viiri@edu.jyu.fi
[1]
[2]
ABSTRACT
We describe progressions of mental models of secondary students for a “case”
physical science topic – magnetism. Secondary students in Finland (N=19) and in the
United States (N=67) engaged in a series of six lessons designed to target aspects of
magnetism known to challenge learners (e.g., the confusion of magnetism with
charge), the structure and organization of matter (e.g., alignment and magnetic
domains), and magnetic fields. Our study included analysis of students applying their
mental models of magnetism to the size dependent behavior of magnetic materials at
the nanoscale. Our findings indicate that, despite identifiable “turning points” in
students’ revisions of their mental models, tenuous non-normative beliefs still
persisted even in the face of repeated trials and conflicting evidence.
1 INTRODUCTION
Magnetism is a phenomenon that fascinates and interests students of all ages and has
been a long standing staple of science curricula in grades K-12 and beyond. Yet, conceptions
of magnetic phenomena have not been investigated as extensively and intensively as other
physical phenomena such as force, electricity, and heat (Guisasola, Almudi & Zubimendi,
2004; Hickey & Schibeci, 1999; Ravanis, Panagiotis, & Vitoratos, 2010). To date, however,
there are few studies that have examined the ways in which students’ conceptions of
magnetism are related to one another, or how students revise their mental models in the light
of contradictory evidence and reflection during the learning process.
In this study, we investigated trajectories by which upper secondary students in
Finland and the U.S. constructed, critiqued and revised their mental models of magnetism
across three key concepts– structure and alignment (magnetic domains), the distinction
between magnetism and static charge, and the reciprocal nature in magnetic interactions
(magnetic fields)– as well the effects of scale.
2 THEORETICAL FRAMEWORK
2.1 STUDENTS’ IDEAS OF MAGNETISM.
Researchers have catalogued a range of students’ ideas about magnetism such as (a)
models of magnetism (Borges & Gilbert, 1998; Constantinou, Raftopoulos, & Spanoudis,
2001; Erikson, 1994); (b) the confusion between magnetism and static charge (Borges &
Gilbert, 1998; Hickey & Schibeci, 1999; Maloney, 1985); (c) action at a distance (Bar, Zinn,
& Rubin, 1997); and (d) the concept of field (Bradamante & Viennot, 2007; Guisasola, et al.,
2004; Guth & Pegg, 1994). Concepts of magnetism pose a challenge for learners, as they
require higher levels of cognition and mental imagery than more concrete and tangible
concepts. The idea of a force being exerted on another without touching, for example, or an
object being attracted equally to either pole of a magnet are counterintuitive for children
2
(Constantinou, et al., 2001). Children commonly view electrostatic and magnetic interactions
as the same phenomenon. The beliefs that the poles of a magnet are oppositely charged, or
that magnetizing involves the transfer or rearrangement of charge, have been revealed from
studies of learners across multiple ages and educational levels (Borges & Gilbert, 1998;
Maloney, 1985; Saglam & Millar, 2006). Likewise, upper secondary and even university
students often believe that the magnetic field has a finite boundary (Bar, et al., 1997), or that
the field lines are a concrete entity (Guisasola, et al., 2004; Guth & Pegg, 1994).
Understanding concepts such as these requires the ability to construct mental models of
abstract concepts, including spatial orientation, noncontact forces and the nature and
organization of matter.
2.2 MENTAL MODELS.
Learning science is to costruct, revise and justify self-constructed mental models, not
simply to adapt models imposed by others and taken for granted (Lehrer, 2009). Mental
models provide the learner a means to organize and make sense of concepts in meaningful
ways to help understand the world (Harrison & Treagust, 1996), and as a representation of
something in the absence of the real thing (Greca & Moriera, 1997), mental models require
the learner to reduce a phenomenon to those elements most meaningful to create a personally
meaningful representation (Gilbert & Boulter, 1995).
The goal of this research was to investigate the progression and coherence of
students’ mental models in learning about magnetism, to answer the questions: (1) What is
the initial nature of secondary students’ mental models of magnetism and magnetic
phenomena? (2) How does the content of students’ models change during instruction? and
(3) What aspects among students’ mental models provide coherent explanatory power across
scale?
4 DESIGN
This study was guided by an interpretive research orientation. We used a quasiexperimental design to compare the construction and progression of mental models of
selected concepts of magnetism.
4.1 PARTICIPANTS
The participants in this study consisted of two samples: (1) a 9th grade chemistry class
in a small university town in Finland (N = 19; 9 male, 10 female), and (2) a 10th-11th grade
physics class in a U.S. mid-western suburban university town (N=65; 38 male, 27 female)..
Neither sample had formally studied magnetism in school prior to this study. The samples
were non-random, solicited from secondary schools with which researchers had previously
collaborated.
4.2 INSTRUCTION
The magnetism unit consisted of six lessons that were focused on a limited number of
concepts, layered to enable students to construct knowledge about magnetism: structure and
organization of matter (magnetic domains), magnetic fields, and magnetic interactions. Our
goal was not to evaluate the effectiveness of the instruction, but rather to document the status
and growth of students’ mental models and explanations of magnetic phenomena in the
context of a classroom learning experience.
4.3 DATA COLLECTION
Data consists of responses to pre- and post-test items, activity journal pages,
embedded assessments, and informal interviews. The post-test was identical to the pre-test
3
and was administered the day after after instruction ended. The assessment items were paperand-pencil, open-ended response and drawing.
4.4 DATA ANALYSIS
We used a constant comparative method to generate and revise codes to characterize
and fit salient features of students’ inscriptions into categories, based on the depth of
understanding exhibited and the characteristics portrayed. Audio recorded interviews were
used for the triangulation of data, as well as to provide a deeper insight into students’
cognition, not accessible from written data alone. Interview audio recordings from the sample
in Finland were transcribed in Finnish and then translated into English.
5 ANALYSIS AND FINDINGS
Four characteristics were used to track the progression of students’ mental models: (1)
elements of static charge, (2) North and South poles, (3) magnetic field, and (4)
representations of magnetic domains (Table 1). Two trends were the result of instruction.
While one of the six lessons pertained specifically to comparing static charge and magnetic
interactions, the U.S. teacher, because of constraints of time, elected not to do this lesson.
Additionally, the Finnish teacher employed the use of a textbook representation of domains in
guiding students through the negation of their mental models, while in the U.S. classes,
students generated their own models. We also note that Finnish students did not refer to poles
by North and South in their initial mental models; they referred to magnets by halves of
different colors (red and white).
Table 1. Magnet characteristics by percent of sample
Finnish
U.S.
Characteristic
Pre
Post
Pre
Post
Static charge
N / S poles
Field
Domains
63%
0%
0%
5%
5%
53%
5%
74%
59%
40%
46%
0%
51%
57%
62%
7%
In the next section, we present two students’ progressions of mental models, one from
Finland, the other from the U.S. We then examine students’ application of their mental
models to scale-related magnetic phenomena.
5.1 ANJA (FINLAND): STATIC CHARGE MODEL TO DOMAIN MODEL
Prior to instruction, Anja based her characterization of magnets on charge. In her
diagram of a magnet she identified poles with signs of charge and wrote captions to explain
what would happen if another magnet was brought near: "If another magnet ( pole is +), it
attracts the other;” and “If another magnet (whose pole is –), it attracts the other."
What a magnet is
“There are different
kinds…but always with a
positive and a negative end;
+ and – poles are
different…and there are
different strengths in
magnets.”
How a magnet works
“It attracts objects to
itself; different poles
attract different signs to
itself or accordingly
repel.”
Magnet characteristics
4
Anja also used her charge model to explain how she believed a magnet is attracted to
either end of a nail,
“Opposite poles are attracted to each other.”
“They repel each other because the poles are
of the same sign.”
A turning point in the revision of Anja’s thinking was the revision of her mental
model to accommodate how a magnetized wire could be cut into pieces, each piece being a
whole magnet. Anja began thinking about internal units of which a magnet might be
composed, observing that each piece of wire has both a north and south pole and that they
behave as magnets, one pole attracted to the other.
“We cut this wire in half and it made separate… magnets, and
they are all alike so that there are no differences. The north
pole directed to the south, just like in that other one.”
Anja’s post-unit responses indicated a more scientifically normative model,
identifying north and south poles, an accurate orientation of field and magnetic domains in
her drawing and accompanying explanation.
“A magnet contains domains that cause a magnetic field outside
the object. If the domains are not aligned, the object no longer
has a magnetic field.”
When Anja applied her emerging mental model to the magnet-nail interaction on the
post-unit assessment, she viewed the nail as remaining magnetized. Contrary to evidence
from the investigations which she conducted, she believed that the nail is attracted to the
magnet in one orientation and repelled by the magnet in the other.
“Different sign domains attract each other.”
“Same sign poles repel each other.”
Anja’s mental model progressed toward a more scientific view. Yet while she adopted
a mental model based on domains, she seemed to have acquired the common belief that
attraction and repulsion are relative to orientation of either the magnet or the object involved
in the interaction; attracted at one end, repelled at the other.
5.2 CHRISTEN (U.S.): STATIC CHARGE MODEL TO MIXED MODEL
Christen’s mental model of magnetism, prior to, throughout and even after the lessons
continued to relate to elements of static charge. She initially defined a magnet as “Something
that is usually made of metal and is charged, and is attracted or repelled to something,” and
affirmed with a drawing that one end (+) of the magnet attracts while the other (–) repels. She
was also not unique in her beliefs that an iron bar can be magnetized by rubbing it with wool
5
and that a balloon rubbed in her hair would act like a magnet. Christen’s pre-unit model of a
magnet and a nail also referred to charge-based interactions.
After she investigated the behavior of a magnetized a paper clip, Christen’s mental
model included aspects of a more normative scientific view of magnetism, with specific
reference to alignment and domains. Yet she maintained her commitment to the influence of
charge in the interaction.
“…the paper clip had the characteristics
of a magnet where the domains are
aligned and when you drop it, the
domains are re-aligned making it not a
magnet.”
Christen’s mental model of magnetism changed little, mixing non-normative and
scientifically normative concepts, contrasted by her post-unit drawings representing the
interaction between a nail and a magnet and final magnet description. In the former, she
replaced signs of charge with North and South poles and indicated that the nail would be
attracted to the magnet in either orientation.
She did not include any indication of domains or field in her drawing, however, so it remains
unclear how she believed the nail could be attracted in either orientation.
Christen’s post-unit drawing and description of a magnet indicated that she adhered to
the notion of charge in her mental model.
“A magnet is something with two oppositely
charged ends that either attract or repel
something.”
While she used a North-South notation of magnetic poles and an (inaccurate) indication of a
magnetic field in her model, Christen still maintained her commitment to charged poles.
5.3 APPLICATION OF STUDENTS’ MENTAL MODELS ACROSS SCALE
The concepts of domains, alignment, field and thermal energy are essential to
understanding the behavior of a magnetic fluid (ferrofluid). Students who incorporated the
concepts of domains into their mental models were able to offer an account for the behavior
of the ferrofluid, based on the mobility of the individual domains. Mikko, for example,
contrasts the arrangement of domains, relative to the placement of the magnet.
“Domains are mixed in there.”
“They are ordered.”
“They are ordered.”
The domain concept was the lynchpin component of students’ mental models that allowed
them to explain this behavior in a manner coherent with the behavior of magnets and
magnetic materials.
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When asked to explain which would be less likely to remain magnetized, a nanoscale
particle or a larger piece, students were more likely to think in terms of the total number of
atoms or domains in the piece, than to consider the effects of thermal energy and the relative
number of surface to interior atoms. For example, Anja reasoned for the larger piece “It has
more domains than the others.” Ben referred to the smaller piece losing its magnetism citing,
“Fewer of the atoms in the smaller one would need to move out of their alignment to disrupt
the magnetic field, so the smaller one.” Galeb indirectly referred to thermal energy, “The
smaller cluster because there are more magnetic orientations that could be disrupted around
the outside of the cluster vs. the inside.” Students who maintained charge in their mental
models attempted to account for the effects of size relative to charge, “Because there is less
space inside for the charges,” and “It’s so small they can’t hold a charge.”
6 CONCLUSIONS
We observed several trends in students’ emerging mental models of magnetism. One
such concept is the persistent belief, despite investigations and evidence to the contrary, that
one side of a magnet attracts an object, the other side repels. Likewise, students continued to
include components of static charge, even incorporating charge into more sophisticated
concepts such as magnetic fields and domains.
We also found that, despite investigating the characteristics of magnetic fields, and
then using the presence of a field as the identifying characteristic of a magnetized object,
students were not likely to incorporate the effect of the field in their mental models of
magnetic interactions between magnets and other objects.
There were two “turning points” which were significant in students’ revisions of their
mental models. As cited above, Anja’s concept of the domain as an internal unit or magnetic
“entity” emerged from her magnetizing and cutting a wire. Likewise, Galeb’s understanding
of domains and their role in the process of magnetization emerged from an activity modeling
domains as iron filings confined to a drinking straw, “In the fresh unmagnetized [straw]
magnet the domains are not aligned in the same direction and after being magnetized the
domains all align in the same direction.”
Our research contributes important theoretical information about the nature of
students’ developing mental models of magnetism. This study serves as a starting point in an
ongoing research program that aims to develop cognitively grounded and research-based
physical science curricula organized around a limited number of key principles. Additionally,
we hope that it can inform the development of physical science curricula that fosters the
development of coherent understanding across size and scale.
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